7. For what value of p does 122p-1 = 5(3.7)p ?
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A. (ln 5 - ln 12)/(ln 3.7 - ln 12) |
B. (ln 5 + ln 12)/(2 ln 12 - ln 3.7) |
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C. (ln 12)/(2 ln 12 – 5 ln 3.7) |
D (ln 12)/(ln 12 – 5 ln 3.7). |
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E. (ln 12 - ln 5)/(2 ln 12 + ln 3.7) |
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Solution: The answer is B
Using the properties of logarithms solve for p as follows:
Given,
Take the natural logarithm of both sides of the above equation,
Since, ln (uv) = ln u + ln v and ln un = n ln u, the above equation can be rewritten as follows,
Solving for p yields,
